Question

Current flows due north in a horizontal transmission line as shown in the figure. Magnetic field at a point $\text{P}$ vertically above it is directed

• A. northwards
• B. southwards
• C. towards east
• D. towards west

Answer 1

The correct option is C towards east

Taking the reference axis $x,y,z$ as shown below.


The current element vector $\left(\overrightarrow{dl}\right)$ for the transmission line is along y-axis.
The direction of $\overrightarrow{dl}$ is along $\hat{j}$
The direction of position vector for point P is along $\hat{k}$.


From Biot-Savart's law at point $\text{P}$,

$\overrightarrow{dB}=\frac{{\mu }_0}{4\pi }i\frac{(\overrightarrow{dl}\times \overrightarrow{r})}{r^3}$

The direction of magnetic field at $B$ is given by,

$\overrightarrow{dl}\times \overrightarrow{r}$
or, direction of $\overrightarrow{dB}\Rightarrow \hat{j}\times \hat{k}=\hat{i}$

$\therefore$ Direction of field at point $\text{P}$ is towards east.

$\text{Alternate method}:$

The direction of magnetic can also be determined using "Fleming's right-hand thumb rule".


In the question, current is from south to north, and hence the direction of the magnetic field would be in the direction of the curl of the fingers. This is represented in the diagram shown.

Thus, the direction of the magnetic field point $P$ is towards east.

$\begin{array}{c}\text{Why this question?}\\ \text{Tip: The direction of}\overrightarrow{B}\text{at any point can be obtained by applying biot savart law and assigning the current element vector}\overrightarrow{\left(dl\right)}\text{in the direction of current}\\ \text{Concept: The direction of magnetic field will be given by direction of}\overrightarrow{dl}\times \overrightarrow{r}\end{array}$